A computer password is required to be 5 characters long. How many passwords are possible if the password requires 2 letter(s) followed by 3 digits (numbers 0-9), where no repetition of any letter or digit is allowed?
Oh, passwords, the key to unlocking our digital lives! Let's do some password math, shall we?
We have 26 letters in the alphabet, and we need to choose 2 of them without repetition. So for the first two characters, we have 26 options for the first letter and 25 options for the second one (since we can't repeat). Multiplying those two together, we get 26 * 25 = 650 possible combinations for the letters.
Moving on to the digits, we have 10 options (0-9) for each of the 3 characters. So, we need to multiply 10 by itself 3 times, which gives us 10^3 = 1,000 possible combinations for the digits.
To get the total number of passwords, we just need to multiply the combinations for the letters by the combinations for the digits: 650 * 1,000 = 650,000 passwords.
Voila! There you have it, 650,000 possible passwords! Just remember to make it something memorable, like "ILuv2Laugh!" - See what I did there? Stay funny and stay secure!
To calculate the number of possible passwords, we can break down the steps:
Step 1: Number of ways to choose 2 letters from the alphabet (26 letters)
Since repetitions are not allowed, we can use the formula for combinations:
Number of ways to choose 2 letters = 26C2 = (26 * 25) / (2 * 1) = 325
Step 2: Number of ways to arrange the chosen 2 letters
Since the order matters, we can use the formula for permutations:
Number of ways to arrange 2 letters = 2P2 = 2! = 2 * 1 = 2
Step 3: Number of digits to choose from (0-9)
Since repetitions are not allowed, we have 10 choices (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) for each digit.
Step 4: Number of ways to arrange the 3 digits
Since the order matters, we can use the formula for permutations:
Number of ways to arrange 3 digits = 3P3 = 3! = 3 * 2 * 1 = 6
Step 5: Multiply the results from steps 2 and 4 together
Number of possible passwords = Number of ways to arrange 2 letters * Number of ways to arrange 3 digits = 2 * 6 = 12
Therefore, there are 12 possible passwords if the password requires 2 letters followed by 3 digits, with no repetition of any letter or digit allowed.
To find the number of possible passwords, we need to consider the choices for each position in the password.
For the first position, we need to choose 2 letters out of the total 26 letters in the English alphabet (assuming the password is case-insensitive). This can be done using combinations. The number of combinations of choosing 2 letters out of 26 is given by:
C(n, r) = n! / (r! * (n - r)!)
where n is the total number of letters (26) and r is the number of letters we want to choose (2).
So, for the first position, we have C(26, 2) = 26! / (2! * (26 - 2)!) = 26 * 25 / 2 = 325 choices.
For the second position, we need to choose 1 letter out of the remaining 24 letters (since we already used 2 letters in the first position). Again, this can be done using combinations.
C(n, r) = n! / (r! * (n - r)!)
where n is the remaining number of letters (24) and r is the number of letters we want to choose (1).
So, for the second position, we have C(24, 1) = 24! / (1! * (24 - 1)!) = 24 choices.
For the third, fourth, and fifth positions, we need to choose digits from 0 to 9. Since no repetition of any digit is allowed, the number of choices for each position is simply the number of available digits.
So, for the third, fourth, and fifth positions, we have 10 choices each.
To calculate the total number of passwords, we need to multiply the number of choices for each position:
Total number of passwords = choices for position 1 * choices for position 2 * choices for position 3 * choices for position 4 * choices for position 5
Total number of passwords = 325 * 24 * 10 * 10 * 10
Total number of passwords = 7,800,000
Therefore, there are 7,800,000 possible passwords that satisfy the given conditions.
well I will do digits and you can do the letters the same way and then multiply
you have 10 digits
first one -- 10 choices
second one --- 9 choices
third one ---- 8 choices
so 10*9*8
now the letters :)